Housing is snapping back faster than many economists had expected, with home builders stepping up production of new homes nationally and fresh foreclosures in California falling to their lowest level since the early days of the bust.

Demand for housing has surged as interest rates have plummeted and home prices in many markets appear to have bottomed, particularly in states such as California where inventories of foreclosures and other lower-priced homes have sunk. The turnaround in prices and record-low supply of newly built homes also are luring builders back after six years of pain.

“The numbers are strong in September, and that is definitely a positive sign,” said Celia Chen, a housing economist with Moody’s Analytics. “It is confirmation that housing is lifting off the bottom.”

Also

Residential construction starts rose 15% nationally last month from August to their highest annual rate in more than four years. A separate report showed that the number of troubled California borrowers entering foreclosure hit its lowest level in the third quarter since the dawning of the mortgage meltdown.

If the gains in housing hold, they could give consumer confidence a boost and help the broader economy recover. Housing has played an important part in lifting the nation out of past downturns but was hampered this time by the severity of the Great Recession and the huge number of vacant and foreclosed homes dragging down the market for years.

Now rising prices are helping homeowners in properties that for several years have been underwater, in which the house wouldn’t bring enough in a sale to pay off the mortgage. Rising values could play a role in lifting household finances if families feel more secure about the direction of the economy.

Any positive economic news presumably would be a boost for President Obama‘s reelection campaign, though both he and Republican challenger Mitt Romney have largely avoided a detailed debate on housing policy. Many on the left have said that Obama’s tepid and patchwork response to the housing downturn resulted in a slower recovery while the right has decried his policies as interventionist failures.

Michael D. Larson, a housing and interest rate analyst for Weiss Research, said the Federal Reserve‘s policies to keep mortgage interest rates low and Obama’s foreclosure prevention efforts have played some role in the recovery — but the improvements can mostly be attributed to natural market dynamics.

“It is certainly encouraging; housing has been this lead anchor around the economy’s neck,” he said. But “most of this is just the passage of time. I think if the Fed or the government had done absolutely nothing … we still would have seen some demand return.”

Several recent trends have underscored improvement in housing. Nationally, home builder stocks are up, prices have begun a modest recovery, and sales of newly built and previously owned homes have risen.

The Commerce Department reported Wednesday that construction of houses and apartment buildings rose in September to a seasonally adjusted annual rate of 872,000, marking the third straight month of improvement. The figures surpassed economists’ expectations of about a 770,000 annual rate.

September had the best monthly performance since July 2008, when housing starts were on an annual pace of 923,000. Compared with September 2011, new housing starts jumped 34.8%, the Commerce Department said.

Last month’s growth was “surprisingly strong,” said David Crowe, chief economist at the National Assn. of Home Builders. “As consumer confidence rises and jobs return, more local markets and more consumers will join the buyer market, and I expect housing construction to continue a modest but fairly steady rise throughout 2013 and into 2014.”

The annual rate of new home groundbreaking still is far below the peak of more than 2.2 million units reached in early 2006 during the housing bubble. But the pace has picked up dramatically from the low of 478,000 in April 2009, and is up sharply from the 706,000 annual rate in May. Building permits for private housing construction, a sign of future activity, also jumped in September, up 11.6% from August and 45.1% from a year earlier. The annual rate in September was 894,000 building permits.

Patrick Newport, an economist with IHS Global Insight, said the increases were likely due to gains in household growth after years of people doubling or tripling up to wait out the worst of the downturn.

“What’s kicking in right now is simply the demographics,” Newport said. “We have been building at too low a rate for four years, and so demand has been suppressed because of the recession, and now it is starting to kick in.”

On the other side of the housing pipeline, the shortage of cheaply priced homes in California appears poised to continue. The number of Californians entering foreclosure dropped in the third quarter to its lowest level since early 2007, according to a report from real estate firm DataQuick. Foreclosure filings have fallen as banks work toward completing more loan modifications and short sales. An improving economy and rising prices have also helped.

“Prices in most areas today are up significantly from their low point in early 2009,” said John Walsh, president of DataQuick. “Additionally, during the past year, we’ve seen short sales overtake the foreclosure process as the procedure of choice to deal with homeowner distress.”

Notices of default fell 10.2% from the prior quarter and 31.2% from the same period last year, DataQuick reported. A total of 49,026 notices of default — the first stage of foreclosure in California — were filed on homes in the Golden State last quarter.

That was the lowest number since the first quarter of 2007, and a 63% decline from the first quarter of 2009, when notice of default filings peaked in the state.

The number of homes lost to foreclosure rose 5% from the prior quarter and dropped 41% from a year earlier. A total of 22,949 homes were lost to foreclosure last quarter.